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Find the equation of the straight line whose distance from origin is 4units and the normal from the orgin to the straight line makes an angle of 135^{\circ }\, with the X-axis in positive direction.


p=4,\alpha =135^{\circ }\, in the equation

x\cos \alpha +y\sin \alpha =p\,

we get

x\cos 135^{\circ }+y\sin 135^{\circ }=4\,

x{\frac  {-1}{{\sqrt  {2}}}}+y{\frac  {1}{{\sqrt  {2}}}}=4\,

x-y+4{\sqrt  {2}}=0\,

Main Page:Geometry:Straight Lines-I